1st what does this situation refers to?
1 answer:
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Linear function rule in terms of x and y for this line is y = x + 12
<em><u>Solution:</u></em>
Given that a line goes through the points (4, 16) and (7, 19)
To find: linear function rule in terms of x and y for this line
A linear function is a function of the form f(x) = ax + b, where a and b are real numbers. Here, a represents the slope of the line, and b represents the y-axis intercept
<em><u>The slope intercept form is given as:</u></em>
y = mx + c
Where "m" is the slope of line and "c" is the y - intercept
Let us first find slope of line
<em><u>The slope "m" of a line is given as:</u></em>
Thus the slope of line is 1
Substitute m = 1 and (x, y) = (4, 16) in y = mx + c
16 = 1(4) + c
c = 16 - 4 = 12
Substitute c = 12 and m = 1 in slope intercept form
y = 1x + 12
y = x + 12 is the required linear function rule
To find the equation, for the x-intercepts at (2, 0) and (4, 0) and a y-intercept of (0, –16) we have to find the nature of the curve.
The correct option is f(x) = –2(x – 2)(x – 4).
Given:
The x-intercepts at (2, 0) and (4, 0).
The y-intercept of (0, –16).
The nature of the graph is quadratic curve. Write the general equation for x-intercept.
Where is number
Substitute 0 for .
We have y-intercept of (0, –16).
The equation would be,
Thus, the correct option is f(x) = –2(x – 2)(x – 4).
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